Theoretical framework and experimental procedure for modelling mesoscopic volume fraction stochastic fluctuations in fiber reinforced composites

Many engineering materials exhibit fluctuations and uncertainties on their macroscopic mechanical properties. This randomness results from random fluctuations observed at a lower scale, especially at the meso-scale where microstructural uncertainties generally occur. In the present paper, we first propose a complete theoretical stochastic framework (that is, a relevant probabilistic model as well as a non-intrusive stochastic solver) in which the volume fraction at the microscale is modelled as a random field whose statistical reduction is performed using a Karhunen–Loeve expansion. Then, an experimental procedure dedicated to the identification of the parameters involved in the probabilistic model is presented and relies on a non-destructive ultrasonic method. The combination of the experimental results with a micromechanical analysis provides realizations of the volume fraction random field. In particular, it is shown that the volume fraction can be modelled by a homogeneous random field whose spatial correlation lengths are determined and may provide conditions on the size of the meso-volumes to be considered.     

Rigid nitronyl-nitroxide-labelled anchoring molecules: syntheses, structural and magnetic investigations

The syntheses of two rigid organic molecular rods bearing a nitronyl-nitroxide radical and a terminal nitrogen-based functionality like a pyridine or a cyano group are reported. Both new paramagnetic molecules are fully characterized, including crystal structure analysis. Furthermore their magnetic behaviours in the crystalline state are investigated and their spin concentration corroborate their excellent purity. While the pyridine functionalized rod is synthesized by converting the corresponding benzaldehyde to the phenyl-nitronyl-nitroxide radical, the synthesis of the cyano functionalized rod demonstrates the accessibility of highly sophisticated spin-labelled molecules via cross-coupling reaction with a meta-iodo-phenyl-nitronyl-nitroxide moiety.     

Transparent boundary conditions for a class of boundary value problems in some ramified domains with a fractal boundary

We consider some boundary value problems in self-similar ramified domains, with Laplace and Helmholtz equations. We discuss transparent boundary conditions. These conditions permit computing the restriction of the solutions to domains obtained by stopping the geometric construction after a finite number of steps. To cite this article: Y. Achdou et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

On the prediction of vector-valued random fields and the spectral distribution of their evanescent component

Let (X_m,n)_(m,n)∈Z² be a C^p-valued wide sense stationary process. We study the prediction theory of such processes according to different total orders on Z². In the case of a “rational order”, we give the spectral distribution of the resulting evanescent component and prove that for two different rational orders, the resulting evanescent components are mutually orthogonal.     

Syntheses of pyridine and bipyridine frameworks combining dual fluorescent and magnetic probes

[structure: see text] 2,6-Disubstituted pyridines, 6-substituted 2,2'-bipyridines, and 6,6'-disubstituted 2,2'-bipyridines are readily prepared under mild conditions from 5-(dimethylamino)-1-naphthalenesulfonamide chloride (DANS-Cl) and chloromethyl-nitronyl nitroxide (CH(2)Cl-NIT) starting materials and adequately functionalized building blocks. The syntheses of the pyridine molecules bearing two radicals and a DANS fragment first required the attachment of the aliphatic radical onto an aldehyde-protected dansylated compound, followed by the construction of the second aromatic radical.     

MECHANISM OF PHOTOOXYGENATION OF THE CD (II) COMPLEX OF PYROPHEOPHORBIDE A METHYL ESTER

Photooxygenation of (pyropheophorbidato a methyl ester)cadmium (II) was studied using ^18,18O₂ labeling of the molecular oxygen required for cleavage of the macrocycle. After reductive demetallation of the primary oxidation product (4,5-dioxo-4,5-secopyropheophorbidato a methyl ester)cadmium (II), the isotope content of formylbilinone 4a was analyzed by repeated-scan fast atom bombardment mass spectrometry. Comparison of the spectroscopic data of the labeled pigment 4a with the statistical probabilities of¹⁸ O isotope incorporation calculated for four possible reaction mechanisms clearly proves that photooxidative ring cleavage occurred by the one-molecule mechanism, i.e. the terminal oxygen atoms of 4a were derived from one oxygen molecule. Furthermore, a study of the exchange of the¹⁸ O-labeled atoms revealed that no exchange occurs within the pH 4.5–9.5 range. In stronger alkaline or acidic solutions, only the oxygen atom of the formyl group is exchanged. Hydrolysis of the methyl ester group of 4a was achieved, without loss of the¹⁸ O label on the formyl group, at pH 7.2 in the presence of pig liver esterase.